Question

*If diagonal of a square is √2 cm then the perimeter of a square is _cm.*

1️⃣ 4
2️⃣ 4√2
3️⃣ 8
4️⃣ 2√2​

Answer 1

Answer:

1️⃣ 4cm

Step-by-step explanation:

x²+x²= (√2)²

2x²= (√2)²

Divide both sides by 2

x²= (√2)²/2

Square root both sides

x = √2 / √2

x = 1

x=1 cm ← 1 side of the square

The perimeter of square=

4 × 1 = 4cm

Hope it helped you.

Answer 2

Option(1) is correct.

Concept:

A square has four symmetry axes and two equal finite diagonals. A diagonal bisection of a square yields two right triangles.

Given:

The length of the diagonal is $\sqrt{2}cm$.

Find:

The perimeter of the square.

Solution:

Take the side of the square as $a$.

Square forms right angle at the vertex. Apply Pythagoras theorem.

$a^2+a^2=(\sqrt{2})^2\\2a^2=2\\a = 1$

The length of the side of given square is $1cm$.

The perimeter of the square is $4a$

$=4*1\\=4cm$

Hence, the perimeter of the square is $4cm$. Option(1) is correct.

Hence, the perimeter of the square is $4cm$. Option(2) is incorrect.

Hence, the perimeter of the square is $4cm$. Option(3) is incorrect.

Hence, the perimeter of the square is $4cm$. Option(4) is incorrect.

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